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The Conservatives have asked police to investigate Labour’s candidate selection process in two further constituencies.

Bob Neill, Tory vice-chairman, has written to Met Commissioner Sir Bernard Hogan-Howe asking him to look into allegations of possible fraud relating to Ilford North and Lewisham Deptford, both in Greater London.

The call comes after Labour handed over evidence to police in Scotland about claims that the Unite union tried to fix the result of a candidate selection in Falkirk by packing the constituency with members, whose subscriptions it paid.

Mr Neill described Falkirk as “the tip of the iceberg”, noting that a leaked Unite document suggested the union was getting involved in the choice of a candidate for the 2015 general election in 41 seats across the country.

In his letter to the Commissioner, Mr Neill said: “I am concerned that this instance is just the tip of the iceberg, as Unite themselves admit they are targeting at least another 40 Labour Party parliamentary selections for similar treatment. Senior Labour Party sources have also confessed that the problems go wider than just Falkirk.”

The Tory MP cited reports that in Ilford North Unite were offering their members free Labour Party membership in exchange for attending a meeting with general secretary Len McCluskey. And he quoted allegations from a Labour London activist that the union was “bankrolling” a number of campaigns, including in Lewisham Deptford.

The new allegations came as Labour leader Ed Miliband came under pressure to take radical steps to curb trade union influence over his party.

He is expected to use a high-stakes speech tomorrow to announce reforms to the way the party is organised - including caps on spending in candidate selections and elections to senior party positions. He has already scrapped a Blair-era scheme under which unions were able to pay the subs of new members which they recruited to the party.

The Labour leader said at the weekend that he wanted to “mend... not end” the link with unions to give more influence to individual members.

But he was plunged into an increasingly bitter public war of words with Mr McCluskey, who warned Mr Miliband to “step back from the brink of a ruinous division” and stop “playing into the hands” of the Tories.

The Unite chief said he would not apologise for efforts to “reclaim Labour” from an “out of touch elite” but renewed his insistence that Unite was not guilty of any criminal wrongdoing.

Labour deputy leader Harriet Harman yesterday admitted the party was looking at “issues” relating to constituencies other than Falkirk - but insisted that allegations that individuals were signed up without their knowledge were confined to the Scottish seat.

Ms Harman said reforms such as the spending cap would be “a significant change for the right reasons” by opening the way to less well-off candidates unable to secure union backing.

Other changes reported to be on the table include the use of “open primaries”, where all voters in a constituency can choose a general election candidate from a party shortlist, not just Labour members.

Former deputy prime minister John Prescott called on Mr Miliband to drop opposition to more state funding for political parties to stop unions - and wealthy Tory backers - “dictating what they think is the position”.

And ex-cabinet minister Lord Reid said the row was based in an “ideological battle” over the future of the party.